Inverse problems for elliptic equations with power type nonlinearities
Year of publication
2021
Authors
Lassas, Matti; Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko
Abstract
We introduce a method for solving Calderón type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not known. Assuming the knowledge of a nonlinear Dirichlet-to-Neumann map, we determine both a potential and a conformal manifold simultaneously in dimension 2, and a potential on transversally anisotropic manifolds in dimensions . In the Euclidean case, we show that one can solve the Calderón problem for certain semilinear equations in a surprisingly simple way without using complex geometrical optics solutions.
Show moreOrganizations and authors
Publication type
Publication format
Article
Parent publication type
Journal
Article type
Original article
Audience
ScientificPeer-reviewed
Peer-ReviewedMINEDU's publication type classification code
A1 Journal article (refereed), original researchPublication channel information
Parent publication name
Publisher
Volume
145
Pages
44-82
ISSN
Publication forum
Publication forum level
3
Open access
Open access in the publisher’s service
No
Self-archived
Yes
Other information
Fields of science
Mathematics
Keywords
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Publication country
France
Internationality of the publisher
International
Language
English
International co-publication
Yes
Co-publication with a company
No
DOI
10.1016/j.matpur.2020.11.006
The publication is included in the Ministry of Education and Culture’s Publication data collection
Yes